Two equations with two unknowns

You can make your own spreadsheet or download mine. This is a handy aid for many of our problems that develop two equations with two unknowns.

We will solve the following simultaneous equations using a spreadsheet:

5 x + 2 y = 23
3 x -   y  = 5
First we will solve by hand and then transfer our operations into spreadsheet notation. The file twoeqn.xls that you can download from our archive has this problem. We multiply each term in the first equation by -3/5. This will cause the x terms to be equal but opposite in sign.
-3 x - 1.2 y = -13.8

Next we sum the second equation with the new equation to get:

-2.2 y = -8.8 	which gives y = 4.
Substituting back into either equation, we find that x = 3. Of course, there are other methods for solving simultaneous equations, but this is easy to follow.
bungah@rpi.edu December, 1997